Mathematical instrument.



No. 866,432. PATENTED SBPT.17, 1907.

i L. A. CLAPR- MATHEMATICAL INSTRUMENT;

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PAT ENTED SEPT. 17', 1907.

, 'L. A. OLAPP. MATHEMATICAL INSTRUMENT.

APPLICATION FILED NOV. 1. 1905.

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LEANDER ALSTON OLAPP, OF THE UNITED STATES NAVY.

MATHEMATICAL INSTRUMENT.

Specification of Letters Patent.

Patented Sept. 17, 1907.

Application filed November 1,1905. Serial No. 285,475-

To all whom it may concern:

Beit known that I, LEANDER ALsroN GLAPP, of the United States Navy, auxiliary service, a citizen of the United States, and a resident of the town of Avon, in the county of Norfolk and State of Massachusetts, have invented a new and Improved Mathematical Instrument, of which the following is a full, clear, and exact description.

My invention relates to a mathematical instrument for solving spherical triangles and similar work.

The principal object of the invention is to provide means for performing a wide variety of calculations and doing away with the use of logarithmic tables for this purpose.

The instrument may be said to afford means for providing a graphic solution of problems of the character indicated above.

With these objects in view, I construct a device having a plurality of members adjustably connected together, each member being adapted to represent an element of a spherical triangle or other geometrical figure to be solved.

Reference is to be had to the accompanying drawings forming a part of this specification, in which similar characters of reference indicate corresponding parts in all the figures.

Figure l is a front elevation partly broken away, of an i instrument constructed in accordance with the principle of my invention; Fig. 2 is a vertical central sectional view of the same, certain parts being in different position and certain parts being removed; Fig. 3 is a plan of a portion of the device with parts broken away; Fig. 4 is a plan of an attachment which can be applied to the main part of the instrument; Fig. 5 is a fragmentary sectional view of a portion of the instrument, showing the application of the attachment illustrated in Fig. 4; and Fig. 6 is a plan of a detail. Fig. 7 is a diagrammatic representation of the arrangement of the apparatus. 7

The main part of the instrument comprises three elements,two limbs a and b, and a curved bar 0. The two limbs a and b are in the form of a pair of flat frames pivotally connected together by means of a hinge d. These two frames are provided with circular scales (1 and b respectively. These two scales constitute the edges of the frames and are drawn on an arc'from the center of the hinge by means of which the two frames are connected. They are designed to represent two great circles. Rig-idly mounted upon one of the frames is a curved bar 0, which passes through an opening in the other frame and is formed on a circle having the axis of the hinge d as its center. It will be obvious that the frames 11 and b can be swung about the hinge, being steadied and guided by the curved bar e, and that either the scale a or b moving toward the other will describe an arc of a great circle at its center. 0011- sequently, if we suppose that the frame b moves toward or from the frame a, the scale I) will describe a portion of the surface of a sphere. In order to provide for this motion and to accurately adjust the angular position of the frame b with respect to the frame a, a projection b is mounted on the frame I), and is perforated to allow the passage of the bar a. The tubular member a is mounted to slide on the bar a, and is adapted to be socured to it by a set-screw 0 An adjusting screw 6 is provided, making accurate adjustments between these two members. The bar e is scaled, and a Vernier is preferably provided for the purpose of accurate reading.

On the scale I) is placed a Vernier-f, which is adapted to be adjusted by means of a screw g along the scale. The scale a is also provided with a vernier h mounted on a bracket h and adapted to be operated by an adjusting screw If. The bracket h is provided with an extension 72 adapted to be secured to the bracket by screws h". This extension is spaced from the bracket so that a ball 70 can be secured between these two parts, this ball constituting a universal joint for the bar a. This bar is provided with a scale, and with means for registering with the scale 1%, said means being shown in the form of a rider m. This rider is provided with projections m adapted to engage in slots 0 in a plate 0 located on the upper side of the bar. It is also provided with a set-screw 0 for holding it in position, and

with a point 0 for registering with the scale b It will also be seen that in addition to the adjustments of the frame a and b the bar 0 can be placed not only parallel with the bar 6 but at an angle thereto, so that a complete spherical triangle is represented by the several members described.

For the purpose of showing the angle between the bar 0 and the scale I), or between the bar 0 and the scale a, I provide an attachment, shown in Figs. 1,

4 and 5, to be substituted for the rider m. The plate 0 is used as before, and to it is secured a semi-circular convex disk p. This disk is provided with a scale about its edge, and with a,straight edge 7) adapted to register with the center line of the bar 0. It is also provided with a screw p for holding it in position, and I with a nut p fitting the screw and holding a pointer 10 thereon. In the use of this attachment the line p is placed parallel or coinciding with the center of the bar 0, and the pointer p is moved to a position parallel with the scale a or b, as the case may be. This pointer then indicates the angle between the two elements on the scale located on the disk.

An instrument constructed in accordance with the principles set forth above provides means for representing all of the different parts of a spherical triangle, consequently, with the necessary number of parts known, the unknown functions can be obtained by reading directly upon the several scales described. It is especially valuable for making calculations used in navigation and it will not be necessary to describe the different problems which can be solved by its use. One example will suffice:

To find the true azimuth, set the instrument with 5 the hour-angle reading on the scale located on the 50 where observations are taken.

bar e, the latitude on the scale I), the declination on the scale a. Swing the rod 0 so that the pointer o is directly opposite the indicated latitude on the scale I), then apply the azimuth attachment to the top of the plate 0 and swing the arm 1) parallel to the scale I), the line p being parallel with the center of the bar 0. This pointer will then register the true azimuth on the semi-circular scale. By the hour angle is understood the elevation of the object at the time at which the observation is taken.

If it is desired to find the hour angle of any heavenly body, that is, the time that the body is from the me- 1 ridian, observations are taken and the declination of that body north or south-of the equator is marked on the scale a by moving the support for the rod 0 the proper distance to the right or left of the center. The observed altitude of the heavenly body as determined is marked on the rod 0 by moving the pointer 0 along said rod for the proper distance. The north or south latitude of the place at which the observations are taken is set off on the scale I) by moving the vernier f to the right or left of the center for the proper distance. The scales at and b are then moved relatively to each other on the hinge d and the rod 0 is moved on its universal joint until the pointer 0 carried by said rod may be brought into engagement with the proper point on the vernier f. By placing the attachment p over the universal joint of the rod c, the angle between said rod and the scale a may be read, and

this angle is the hour angle or time. If it is desired to the azimuth thus determined.

In general the same parts of the instrument are usually employed to indicate the quantities represented in the above example, but this is not absolutely necessary in all cases. When used for such calculations as this the instrument saves about threequarters of the time and labor at present used in calculations for navigation. The hour-angle can be computed in less than a half a minute, rendering it especially valuable to fast steamships and all crafts For the student it illustrates the principle of these calculations in a graphic and clear manner, while it makes all calculations for the man who knows little of navigation, without requiring any great expenditure of time,

The use of the instrument can be learned by a person unskilled in mathematics, in much less time than the use of logarithmic tables. Furthermore, when logarithmic calculations are employed, a mistake isvery diflicult to find, and much time is necessarily consumed when calculations do not result correctly.-

With this instrument it is not easy to make a mistake, and if one should be made it would be seen at a glance. The instrument may be supported in any desired manner and I have not illustrated any particular support. The various movable elements may also be provided with handles for convenience in operation, and the verniers preferably have magnifying glasses.

Having thus described my invention, I claim as new and desire to secure by Letters Patent:

1. A mathematical instrument, comprising a pair of frames pivoted together, a curved scale on each frame, means for adjusting the frames toward and from each other about their pivots, a bracket adjustable along one of said scales, and a scaled bar connected with said bracket by a universal joint.

2. A mathematical instrument, comprising a frame having a semi-circular scale thereon, a bracket adjustable along said scale, a curved bar connected with said bracket by a universal joint, and a frame adjustably connected with the first frame and having a semi-circular scale thereon.

8. A imithematical instrument comprising a pair of frames pivoted together upon a central line, each frame having a selnicircular scale drawn upon said line as a diameter. means for adjusting the frames at varying angles with respect to each other, and a curved graduated bar adjustably secured to one of said frames and having a pointer adjustable thereon, said pointer being adapted to cooperate with the scale upon the other frame, as and for the purpose set forth.

4. A mathematical instrument, comprising a pair of frames pivoted together upon a central line, a semi-circular scale on each frame drawn upon said line as a diameter, a curved bar secured to one of said frames and drawn on an arc with said line as a center, the other frame being provided with a perforation for receiving said bar, and

means for adjusting the second frame along said bar;

said means comprising a slide adapted to be secured to the bar in any position, and a screw connected with said slide and with the second frame.

A mathematical instrument. comprising a frame having a semi-circular scale thereon, a bar curved on an are drawn from the center of said semi-circular scale, a universal joint for connecting said bar with said frame. and an attachment for said bar comprising a plate having an er ge adapted to coincide with the center of said bar and a semi-circular scale for indicating the angle between said bar and any other part of the instrument.

6. A mathematical instrument comprising a frame having a semicircular scale thereon, a bar curved on an are drawn from the center of said semicircular scale, a liniversal joint for connecting said bar with the frame, and means on the bar for registering with the scale.

7. A mathematical instrument comprising a frame having a scale thereon, a bar, means for movably connecting the bar with said frame, and an attachment for said bar comprising a plate having an edge adapted to coincide with the center of the bar, a scale for indicating the angle between said bar and any other part of the instrument A mathematical instrument comprising a pair of frames pivoted together, each frame having; a scale, a curved bar secured to one of said frames, and means for adjusting .ic second frame along said bar, said means comprising a slide adapted to be secured to the bar in any position, and a screw connected with said slide and with the second frame.-

in testimony whereof I have signed my name to this specification in the presence of two subscribing witnesses.

LEANDER ALSTON CLAPR Witnesses FRED E. Hon'roN,

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